Improved validation index for fuzzy clustering

This paper proposes a new validation index for fuzzy clustering in order to eliminate the monotonically decreasing tendency as the number of clusters approaches to the number of data points and avoid the numerical instability of validation index when fuzzy weighting exponent increases. Limit analyses of Xie-Beni index, Kwon index and the proposed index are also considered for the convenience of contrast. Lastly, two numerical examples are presented to show the effectiveness of the proposed validation index.